He won us the European Cup. With regards to football he's earned the right to do as he wants as far as I'm concerned. It's not going to diminish what happened in 2005, or make me feel any different about it. Nor the FA Cup in 2006, the latter European Cup runs or the fact he got us close to the League Championship in 2009.
Would I be arsed if he ended up winning something with them? Probably not. I mean it's unlikely as they're a million miles away from competing for the big prizes, but he could get them a cup maybe. If he does then so what? Other teams win stuff, it happens. Supporting Liverpool, especially right now under Klopp, is about supporting Liverpool not caring about what others are doing. Having a bit of a chuckle at other's misfortune is an added benefit, but if those chuckles dry up a little, then it's hardly the end of the world.